Benjamin M. Sanderson and Gokhan Danabasoglupeople.oregonstate.edu/~shellk/AJonko_Manuscript_2012_revised.pdf · Simulations with aslab ocean model(SOM) version ofthe GCMare used

Generated using version 3.1.2 of the official AMS LATEX template

Climate feedbacks in CCSM3 under changing CO2 forcing. Part1

II: Variation of climate feedbacks and sensitivity with forcing.2

Alexandra K. Jonko ∗ and Karen M. Shell

Oregon State University, Corvallis, Oregon

3

Benjamin M. Sanderson and Gokhan Danabasoglu

National Center for Atmospheric Research, Boulder, Colorado

4

∗Corresponding author address: Alexandra K. Jonko, College of Earth, Ocean and Atmospheric Sciences,

Oregon State University, 104 CEOAS Admin. Bldg., Corvallis, OR 97331-5503.

E-mail: [email protected]

1

ABSTRACT5

Are equilibrium climate sensitivity and the associated radiative feedbacks a constant property6

of the climate system, or do they change with forcing magnitude and base climate? Using7

the radiative kernel technique, feedbacks and climate sensitivity are evaluated in a fully8

coupled general circulation model (GCM) for three successive doublings of carbon dioxide9

starting from present day concentrations. Climate sensitivity increases by 23% between the10

first and third CO2 doublings. Increases in the positive water vapor and cloud feedbacks are11

partially balanced by a decrease in the positive surface albedo feedback and an increase in12

the negative lapse rate feedback. Feedbacks can be decomposed into a radiative flux change13

and a climate variable response to temperature change. The changes in water vapor and14

Planck feedbacks are due largely to changes in the radiative response with climate state.15

Higher concentrations of greenhouse gases and higher temperatures lead to more absorption16

and emission of longwave radiation. Changes in cloud feedbacks are dominated by the17

climate response to temperature change, while the lapse rate and albedo feedbacks combine18

elements of both. Simulations with a slab ocean model (SOM) version of the GCM are used to19

verify whether a SOM-GCM accurately reproduces the behavior of the fully coupled model.20

Although feedbacks differ in magnitude between model configurations (with differences as21

large as those between CO2 doublings for some feedbacks), changes in feedbacks between22

CO2 doublings are consistent in sign and magnitude in the SOM-GCM and the fully coupled23

model.24

1

1. Introduction25

It has been suggested that climate sensitivity, the Earth’s equilibrium surface tempera-26

ture response to an external perturbation, is a constant property of the climate system, that27

remains unchanged under different forcing magnitudes and types. Indeed, several previous28

model studies find little to no dependence of climate sensitivity on forcing (Chen and Ra-29

maswamy 1996; Forster et al. 2000; Boer and Yu 2003; Hansen et al. 2005). More recent30

work exploring a broader range of forcing (Boer et al. 2005; Colman and McAvaney 2009)31

suggests trends in climate sensitivity as external perturbations increase. However, these32

trends are not consistent among the studies, with each using different models, forcing agents33

and methodologies.34

Colman and McAvaney (2009), CM09 hereafter, use the partial radiative perturbation (PRP)35

method (Wetherald and Manabe 1988) to examine individual feedbacks in the Australian36

Bureau of Meteorological Research Centre (BMRC) atmospheric general circulation model37

(GCM) coupled to a mixed layer ocean model in response to CO2 forcing ranging from 1/1638

to 32 × present day values. They find that, while the radiative forcing increases with base-39

line CO2 amount, climate sensitivity decreases and identify a reduced albedo feedback as40

the main source of this decrease.41

Boer et al. (2005) employ changes in solar constant as a forcing analog to CO2 changes to in-42

vestigate the response of climate sensitivity in the National Center for Atmospheric Research43

(NCAR) Climate System Model (CSM) and detect an increase in climate sensitivity with44

increasing forcing for solar constant changes up to 25%. For larger changes, they observe45

a runaway effect associated with cloud changes and the shortwave (SW) cloud feedback in46

particular.47

Both of these studies, like most work investigating the relationship between climate sensi-48

tivity and forcing, use atmospheric general circulation models (AGCMs) coupled to a slab49

ocean model (SOM). Simulations with this setup equilibrate quickly, even for very large per-50

turbations. However, they do not permit the role of the ocean circulation to be taken into51

2

account explicitly. As pointed out by CM09, similar analyses with fully coupled models are52

required to confirm that SOMs can adequately represent ocean processes relevant to climate53

sensitivity.54

Hansen et al. (2005) investigate the role of the ocean component of a coupled model by com-55

paring climate sensitivity estimates obtained with the Goddard Institute for Space Studies56

(GISS) ModelE coupled to several different ocean models. They obtain comparable estimates57

of climate sensitivity for three ocean models of different complexity. However, the dynamic58

model they use is somewhat simplified (Russel et al. 1995) and results for a fully dynamic59

model are not presented.60

Danabasoglu and Gent (2009) compare equilibrium climate sensitivity in the fully coupled61

NCAR Community Climate System Model version 3 (CCSM3) to its slab ocean version for62

an instantaneous doubling of CO2 concentrations and find that sensitivities are comparable63

within an uncertainty range defined based on interannual variability. Here we extend their64

analysis by including simulations with larger forcing and by evaluating individual feedbacks65

in addition to climate sensitivity. We add two simulations forced with four and eight times66

present day CO2 concentrations. The range of forcing we are able to explore is limited67

compared to CM09, since the fully coupled model takes a much longer time to adjust to an68

imposed perturbation and therefore is much more costly to run.69

We evaluate climate sensitivity and feedbacks for each of the three doublings of CO2 con-70

centrations (2xCO2-1xCO2, 4xCO2-2xCO2 and 8xCO2-4xCO2) using the radiative kernel71

technique extended for large, nonlinear perturbations (Jonko et al. 2012). Additionally,72

we compare feedbacks and climate sensitivity estimates from CCSM and its atmospheric73

component, the Community Atmosphere Model version 3, coupled to a slab ocean model74

(CAM-SOM), to evaluate the accuracy of the slab ocean model for feedback estimates. In75

the next section, we present the model data used in our analysis. Section 3 explains the76

methods used and gives an overview of the order in which results will be presented. The77

impact of varying forcing on individual feedbacks and climate sensitivity is discussed in78

3

sections 4 and 5, respectively. Results are summarized in section 6.79

2. Model Data80

We analyze four simulations of the low resolution NCAR CCSM3, truncated at T31 with81

26 vertical levels (Yeager et al. 2006), for both the full depth ocean (CCSM) and the slab82

ocean (CAM-SOM) configurations. Included are a control run with 1990 CO2 concentra-83

tions of 355 ppmv and simulations in which these concentrations were doubled to 710 ppmv,84

quadrupled to 1420 ppmv and octupled to 2840 ppmv, respectively.85

Figures 1a and b show global average changes in net top-of-atmosphere (TOA) flux (absorbed86

solar minus outgoing longwave radiation) between the three perturbed simulations and the87

control run for CCSM and CAM-SOM. While all CAM-SOM simulations were run for 6088

years, the CCSM 2xCO2 simulation was run for 3000 years - the time scale for adjustment of89

the deep ocean (Danabasoglu 2004; Stouffer 2004) - and the 4xCO2 and 8xCO2 simulations90

were stopped after 2000 and 1450 years, respectively. Years 1 to 1450 are shown for all91

three cases. In the 2xCO2 simulation, the climate system reaches equilibrium with respect92

to the applied forcing after approximately 2000 years. For comparison, all three perturbed93

CAM-SOM simulations reach equilibrium after approximately 25 to 30 years. For the larger94

4xCO2 and 8xCO2 perturbations, the time scale of equilibration for CCSM is longer. Hence,95

the 4xCO2 and 8xCO2 simulations are not in equilibrium at the end of the simulations.96

The remaining net TOA flux imbalance, computed from the average over the last common97

decade of the simulations, 1441-1450, increases from 0.14 W m−2 for 2xCO2 to 0.59 W m−298

for 8xCO2. Figures 1c and d show the surface air temperature change for each doubling in99

CO2 concentration. We are interested in the temperature change per doubling of CO2 rather100

than the change from the control run, because changes in this value indicate deviations from101

linearity in the behavior of the system for successive CO2 doublings. In both model versions102

the temperature change at year 1450 increases in magnitude from 2.2 K for the first doubling103

4

to 3.2 K for the third doubling, an increase of 1 K.104

In CCSM, the global mean surface air temperature increases by 2.2 K in 2xCO2, 4.7 K in105

4xCO2 and by 7.9 K in 8xCO2 relative to the control run for each forced simulation by106

the last common decade of the simulations. For comparison, the equilibrium temperature107

increase in the 2xCO2 simulation totals 2.5 K (based on model years 2991-3000). Values in108

CAM-SOM for the last decade of the simulations (model years 51-60) are almost identical109

at 2.2 K, 4.7 K and 7.8 K.110

111

3. Methods112

The final equilibrium temperature change in response to a forcing depends not only on113

the forcing F itself, but also on the magnitude of the feedback parameter λ.114

F = −

∆R

∆T as

∆T as = −λ∆T as (1)115

Here, R is the net radiative flux (excluding the forcing), ∆T as is the global average change116

in surface air temperature and λ the feedback parameter containing contributions from117

individual feedback processes related to the Planck response (P ) as well as changes in lapse118

rate (LR), specific humidity (q), surface albedo (α) and clouds (C).119

λ = λP + λln(q) + λLR + λα + λC + Re (2)120

ln(q) is the natural logarithm of specific humidity, used to evaluate the water vapor feedback,121

and Re is a residual, containing higher order cross-terms and is relatively small (about 10%;122

Jonko et al. 2012). We use the radiative kernel technique (Shell et al. 2008; Soden et al.123

2008; Jonko et al. 2012) to calculate individual feedbacks. It has been shown that this linear124

technique in its regular form is valid for small perturbations on the order of 2xCO2 (Jonko125

et al. 2012). Since we are dealing with much larger forcings here, we use a combination126

of kernels, based on different climate states, which is more suitable for large, nonlinear127

5

perturbations (Jonko et al. 2012): a present day (1xCO2) base kernel for 2xCO2 - 1xCO2128

feedbacks, an 8xCO2 base kernel for 8xCO2-4xCO2 feedbacks and a combination of both129

(1

21xCO2 kernel +

1

28xCO2 kernel) for 4xCO2-2xCO2 feedbacks.130

To calculate the water vapor and albedo feedbacks we simply multiply the appropriate kernels131

by differences in feedback variable between experiment and control simulations, normalized132

by global average surface air temperature change, dT as.133

λX =∂R

∂X

dX

dT as

(3)134

where X stands for the feedback variables, the natural log of specific humidity and surface135

albedo.136

The Planck feedback is the response of longwave (LW) TOA flux to a perturbation in surface137

temperature that is applied to each vertical layer of the troposphere. It is the sum of the138

atmospheric temperature kernel at every level of the troposphere and the surface temperature139

kernel, both multiplied by the surface temperature change and normalized by dT as.140

λP =∂R

∂Ts

dTs

dT as

+∂R

∂T

dTs

dT as

(4)141

The lapse rate feedback is the response of changing vertical temperature structure to radiative142

perturbations and is computed by taking the difference between the atmospheric temperature143

feedback and the second term of the Planck feedback.144

λLR =∂R

∂T

dT

dT as

−

∂R

∂T

dTs

dT as

(5)145

Because of nonlinearities introduced primarily by cloud overlap, the evaluation of the cloud146

feedback using a cloud kernel is less straightforward. Zelinka et al. (2012) and Sanderson and147

Shell (2012) have calculated cloud kernels. However, such computations require the use of148

output from a cloud simulator, which is not available for the simulations used here. Rather,149

we employ the concept of cloud radiative forcing (CRF), defined as the difference between150

all-sky and clear-sky fluxes (R′−R′

c) (Cess and Potter 1987). R′ differs from R in Equation151

(3) in that it does include the forcing, F . CRF measures the effect of clouds on the radiation152

6

budget for a given climate state. The change in CRF due to an external forcing is often used153

to approximate the cloud feedback (Soden et al. 2004).154

∆CRF = ∆(R′− R′

c) (6)155

∆CRF is a biased estimator of cloud feedback due to its sensitivity not only to cloud changes,156

but also to changes in non-cloud variables (Soden et al. 2004, 2008). Using the kernel157

technique, ∆CRF can be corrected for such biases by subtracting from it the differences158

between all-sky and clear-sky feedbacks,159

∆CRFk = ∆[

(R − Rc)P + (R − Rc)ln(q) + (R − Rc)LR + (R − Rc)α + (F − Fc)CO2

]

(7)160

Here, (F − Fc)CO2is the difference between the all-sky and clear-sky CO2 forcing. While161

∆CRF alone is small and negative in CCSM3, the adjusted ∆CRF is positive and substan-162

tially larger in magnitude, illustrating the large bias of ∆CRF due to changes in non-cloud163

feedbacks. To obtain a cloud feedback, adj.∆CRF = ∆CRF - ∆CRFk is normalized by164

∆T as.165

Other decompositions are equally valid. For example, Zhang et al. (1994) use surface and166

atmospheric temperature as feedback variables rather than the Planck response and lapse167

rate. The radiative kernel technique is not as accurate as the PRP method used by CM09.168

However, it would be impractical to use PRP here, since it requires a set of radiative transfer169

calculations to be carried out for each feedback estimate.170

We compare feedbacks for three successive doublings in CO2 concentration: 355 to 710171

ppmv (2xCO2-1xCO2), 710 to 1420 ppmv (4xCO2-2xCO2) and 1420 to 2840 ppmv (8xCO2-172

4xCO2). For CAM-SOM simulations we use 30-year averages of model variables over the173

years 31 to 60, while 100 30-year means (running averages separated by 10-year intervals)174

from years 431 through 1450 are used for feedback estimates from CCSM simulations. For175

CCSM feedbacks, Figure 2 shows histograms of global, annual 30-year average values for the176

three doublings, binned using 0.01 Wm−2K−1 intervals. Also shown are the overall 1000-year177

averages (squares) and standard deviations (error bars), a measure of the uncertainty in the178

7

estimate of the mean due to interannual and other short term variability. Overall averages179

are compared with CAM-SOM average feedbacks in Tables 1, while differences between dou-180

blings are summarized in Table 2.181

We assess the statistical significance of the differences between the feedback distributions182

using recurrence analysis (von Storch and Zwiers 1988). Rather than testing for differences183

between sample means, this method evaluates the degree of separation between two sample184

distributions. Two random variables are said to be (p,q)-recurrent, if q percent of the prob-185

ability density function of one variable lies outside of p percent of the distribution of the186

other variable. Thus, sample means of two random variables that are (50%,84%)-recurrent187

are separated by one standard deviation (von Storch and Zwiers, 1988; their Figure 4). A188

non-parametric method to test for recurrence involves counting the number of realizations189

of one random variable that lie beyond a threshold, defined as a percentile of the normal190

distribution fitted to the other variable. The most robust such test is to reject the null191

hypothesis of a realization not being attributable to one or the other distribution if the192

smallest realization of one distribution is larger than the largest realization of the other, i.e.,193

there is no overlap between distributions. This is the case for all differences between CO2194

for water vapor and albedo feedbacks and climate sensitivity (Figure 2b, d and h), as well195

as some of the differences in Planck, SW cloud and net cloud feedbacks (Figure 2a, e and196

g). For these cases we reject the null hypothesis and infer that the feedback distributions197

are significantly different. For the remaining cases, we test for (50%,98%)-recurrence, which198

represents a separation of means by two standard deviations. We fit a normal distribution199

to the feedback distribution with the smaller average value and find its 98th percentile, Xp.200

We then count the realizations of the other feedback distribution that are larger than this201

threshold. If the count T equals the sample size n = 100, the difference between feedbacks is202

found to be (50%,98%)-recurrent at significance level qn = 0.98100 = 0.13, or 87%. Xp and203

T are summarized in Table 3.204

Because we are using a different kernel for each CO2 doubling, we can separate the change in205

8

feedbacks between CO2 doublings into a radiative response (changes in kernels) and a climate206

response (changes in feedback variables as a function of surface air temperature change).207

While we can track the change in surface temperature and feedback variables,dX

dT as

, over208

the course of the coupled model runs, we only have one estimate of the kernel∂R

∂Xin each209

case. Hence, the variability in feedback values shown in the individual histograms (Figure 2)210

reflects only the temporal evolution of feedback variable and surface temperature changes,211

but not changes in the radiative flux response.212

To evaluate whether the changes in feedbacks between the individual doublings are due213

to changes in the radiative or climate response, we compute “hybrid feedbacks”, combin-214

ing the 8xCO2 kernel with the 2xCO2-1xCO2 climate response and the 1xCO2 kernel with215

the 8xCO2-4xCO2 climate response, and compare these with the “full” 2xCO2-1xCO2 and216

8xCO2-4xCO2 feedbacks in Table 1. The differences between feedbacks for the first and third217

CO2 doubling are compared with differences between the full 2xCO2-1xCO2 feedback and218

the hybrid feedbacks in Table 2. Their zonal distributions of full and hybrid feedbacks are219

investigated in Figure 3. The kernels used are represented by line type (solid or dashed),220

while the climate response is represented by line color. Thus, solid blue lines are full 2xCO2-221

1xCO2 feedbacks and the dashed red lines are full 8xCO2-4xCO2 feedbacks, while the dashed222

blue lines are hybrid feedbacks computed combining 2xCO2-1xCO2 climate responses with223

8xCO2 kernels and solid red lines are hybrid feedbacks that result from the combination of224

8xCO2-4xCO2 climate responses and 1xCO2 kernels. When lines of the same color lie close225

together, this means that changing the kernel does not impact the feedback. When lines of226

the same type overlap, it follows that feedbacks are insensitive to changing climate responses.227

While the figures and tables introduced here contain results for all feedbacks, we will exam-228

ine each of the feedbacks individually, making reference to the appropriate locations in each229

figure and table, throughout the following sections.230

231

9

4. Radiative Feedbacks232

a. Planck Feedback233

Increasing temperatures at the surface and throughout the atmosphere lead to an increase234

in outgoing longwave LW radiation, which stabilizes the climate system. The Planck feedback235

is defined as the response of LW TOA flux to the perturbation in surface temperature applied236

to each vertical layer of the troposphere. It is the strongest negative feedback, with an average237

value that decreases in magnitude slightly from -3.10 Wm−2K−1 to -3.03 Wm−2K−1 between238

the first and third CO2 doubling in both CCSM (Figure 2a) and CAM-SOM. The larger239

change occurs between the first and second doublings in CO2, showing no overlap between240

distributions, while the change between the second and third doublings is rather small and241

not found to be significant by the recurrence test (Table 3). The decrease reflects changes in242

surface and atmospheric temperature kernels (Jonko et al. 2012), or the radiative response243

(Tables 1 and 2), since the climate response for the Planck feedback isdTs

dT as

≈ 1.244

Thus, in a warmer climate with higher concentrations of LW absorbers, the change in OLR245

for a standard temperature anomaly decreases.246

b. Water Vapor Feedback247

As atmospheric temperatures rise, so does the water vapor content of the atmosphere,248

strengthening the greenhouse effect and resulting in a positive water vapor feedback. This249

feedback,∂R

∂ln(q)

dln(q)

dTas

, is calculated using the change in the natural logarithm of specific250

humidity, since absorption of radiation by water vapor scales approximately linearly with251

the natural logarithm rather than the absolute value of specific humidity (Raval and Ra-252

manathan 1989). The water vapor feedback is strongest in the tropics, where the troposphere253

is close to saturation, but it is positive everywhere (Figure 3b). It increases with baseline254

CO2 concentration, from 1.57 to 1.91 Wm−2K−1 in CCSM. All differences are found to be255

significant, i.e. there is no overlap between histograms in Figure 2b. For CAM-SOM the256

10

feedback increases from 1.64 to 2.03 Wm−2K−1 (Table 1). Since the kernel and global av-257

erage surface air temperature change are the same for both CCSM and CAM-SOM, the258

larger feedback in CAM-SOM is related to a stronger increase in specific humidity in this259

configuration. The increase in feedback with CO2 baseline amount is explained primarily260

by an increase in radiative kernel∂R

∂ln(q)(lines of the same type lie close together in Fig-261

ure 3b), since, for every CO2 doubling, higher concentrations not only of water vapor but262

also of CO2 increase the rate of absorption of LW radiation (Jonko et al. 2012). The climate263

response remains approximately constant, increasing only slightly for successive doublings264

of CO2 and accounting for roughly 20% (CCSM) and 25% (CAM-SOM) of the water vapor265

feedback increase (Table 2).266

c. Lapse Rate Feedback267

The lapse rate feedback measures the impact of a radiative perturbation on the vertical268

structure of atmospheric temperature. The strongest contributions to this feedback stem269

from the radiative effect of a decreasing moist adiabatic lapse rate with surface temperature270

warming that occurs over areas where the troposphere is near saturation. This is the case271

in much of the tropics. Since a smaller lapse rate translates to a stronger warming in the272

upper troposphere and increased upwelling LW radiation from these levels, the lapse rate273

feedback is negative in the tropics (Figure 3c). The decrease in lapse rate is a function of the274

initial surface temperature as well as the temperature change, and the lapse rate feedback275

increases in magnitude with each CO2 doubling along with the starting surface temperature,276

from -0.37 to -0.53 Wm−2K−1 in CCSM. 75% of this increase is explained by the climate277

response, with only a small portion coming from radiative kernel changes. Figure 3c shows278

that the lapse rate feedback at all latitudes is shifted toward more negative values with279

increasing baseline CO2 amount. In the tropics, this increase in negative feedback values is280

due primarily to changes in radiative kernel. Here lines of the same type overlap in Figure281

3c. In the extratropics, however, the decrease in positive values stems mostly from changes282

11

in the surface and atmospheric temperature responses, and lines of the same color lie closer283

together in Figure 3c.284

Histograms for the lapse rate feedback exhibit the largest overlap of all feedbacks, in partic-285

ular between the first and second CO2 doubling (Figure 2c). The separation between these286

two distributions is not found to be recurrent, unlike the differences between the first and287

third doublings, as well as the second and third doublings, which are recurrent.288

Compared with CCSM, CAM-SOM has a stronger lapse rate feedback, which increases in289

magnitude from -0.48 to -0.65 Wm−2K−1 for the first and third CO2 doublings, respectively.290

Note that the difference between CAM-SOM and CCSM feedbacks for individual CO2 dou-291

blings is as large or larger (for 4xCO2 - 2xCO2) than the difference between successive292

doublings for CCSM.293

d. Surface Albedo Feedback294

The surface albedo feedback results primarily from albedo perturbations in areas expe-295

riencing changes in the extent of sea ice and snow cover. As sea ice and snow melt, they296

expose underlying areas, which typically have much lower albedos, leading to more SW ab-297

sorption and further temperature increase. The albedo feedback decreases from 0.29 to 0.16298

Wm−2K−1 in CCSM and from 0.26 to 0.09 Wm−2K−1 in CAM-SOM for the three doublings.299

CAM-SOM feedback values are slightly smaller than in CCSM, because changes in snow and300

sea ice are smaller in CAM-SOM (compare Figures 4a and b). On the global average, the301

albedo change in CAM-SOM is only 50% of that seen in CCSM. The spatial distribution of302

the albedo feedback follows changes in albedo for both models (Figure 4). However, global303

average hybrid feedbacks show that both the climate response and change in radiative kernel304

contribute approximately equally to the decrease in albedo feedback from the 2xCO2-1xCO2305

to the 8xCO2-4xCO2 experiment (Tables 1 and 2). This behavior is supported by the zonal306

distribution of feedbacks in Figure 3d, which shows a decrease in albedo feedback in the307

latitude bands 30◦N-65◦N and 50◦S-70◦S. In both hemispheres, this decrease is explained by308

12

the climate response (i.e. lines of the same color overlap) at lower latitudes. The kernel gains309

more importance at higher latitudes, where lines of the same color begin to diverge, while310

lines of the same type converge. The albedo feedback increases north of 75◦N and south311

of 80◦S. Note that changes at these high latitudes have a small contribution to the global312

mean, since the surface area affected as well as the amount of solar radiation received are313

comparatively small.314

The combined effect (0.13 Wm−2K−1 in CCSM) is larger than the sum of the individual315

changes due to radiative kernel (0.03 Wm−2K−1) and climate response (0.04 Wm−2K−1),316

confirming the importance of nonlinearities for the albedo feedback (Shell et al. 2008). There317

is no overlap between any of the three feedback histograms in Figure 2d, i.e. all differences318

are statistically significant.319

e. Cloud Feedback320

Clouds have competing positive and negative feedback effects on climate. Increases in321

cloud cover lead to more reflection of incoming solar radiation, resulting in a negative global322

average SW cloud feedback if clouds increase with temperature. The CCSM SW cloud323

feedback is negative in the tropics and at high latitudes, and positive at midlatitudes (Figure324

3f). At the same time, more clouds also increase absorption of upwelling LW radiation.325

Assuming that clouds increase with temperature, this results in a positive LW cloud feedback326

with maxima in the tropics and high latitudes (Figure 3e). In CCSM, these effects combine327

to a positive overall cloud feedback. The zonal distribution of the net effect follows that328

of the SW cloud feedback, with positive values in the midlatitudes and negative values in329

the tropics and high latitudes (Figure 3g). The CCSM cloud feedback is 0.06 Wm−2K−1330

for 2xCO2-1xCO2, increasing to 0.24 Wm−2K−1 for 8xCO2-4xCO2. In CAM-SOM cloud331

feedback increases from 0.05 to 0.30 Wm−2K−1.332

Going from the first to second doubling of CO2, the increase in cloud feedback is explained333

by a significant decrease in the negative SW cloud feedback, occurring in the tropics to334

13

subtropics between 10◦ and 30◦N and S as well as an increase in the positive SW cloud335

feedback in the NH midlatitudes. While the positive LW cloud feedback also decreases, this336

change is comparatively small and not recurrent. From the second to the third doubling, both337

the SW and LW cloud feedbacks become slightly more positive. Neither of these changes338

on their own are found to be recurrent. However, the combination results in a significant339

increase in the overall cloud feedback (see Table 1 and Figure 2e, f and g).340

5. Climate Sensitivity and Radiative Forcing341

We sum the Planck, lapse rate, water vapor, surface albedo and cloud feedbacks to342

obtain the feedback parameter λ in Equation (2). This sum is negative, i.e. it is dominated343

by stabilizing contributions from surface and air temperature changes. The residual in344

Equation (2), comprising higher order terms, is calculated explicitly in (Jonko et al. 2012)345

and is ∼ 10%. The negative inverse of the feedback parameter is the climate sensitivity346

s = −1/λ. Average climate sensitivity in CCSM increases with each doubling of CO2, from347

0.65 KW−1m2 to 0.80 KW−1m2. The three distributions are well separated, with no overlap348

between adjacent histograms (Figure 2h). These differences represent a 23% increase in349

average climate sensitivity between the first and third CO2 doubling.350

CAM-SOM climate sensitivities are comparable, but slightly smaller at 0.61 K W−1m2 for351

the 2xCO2-1xCO2 experiment and 0.79 K W−1m2 for the 8xCO2-4xCO2 experiment, a 30%352

increase. While these increases seem to be largely due to the radiative response (Table 2),353

complex interactions - in particular in the case of cloud feedback calculations - make such a354

straightforward interpretation more difficult than for the case of the non-cloud feedbacks.355

The increase in climate sensitivity we see in CCSM and CAM-SOM disagrees with CM09,356

who find that climate sensitivity decreases with each subsequent CO2 doubling. In their357

model (BMRC), the increase in water vapor feedback is offset close to completely by an358

increase in lapse rate feedback, and the decrease in climate sensitivity is explained by a359

14

decreasing albedo feedback. In CCSM, the sum of water vapor and lapse rate feedbacks360

increases in magnitude rather than remaining constant, so that the increase in water vapor361

and cloud feedbacks outweighs the comparatively small decrease in albedo feedback.362

Assuming equilibrium, we can substitute λ = −1/s into Equation (1) to obtain a relationship363

between climate sensitivity and radiative forcing, F :364

F =∆T as

s(8)365

Forcing values obtained for CCSM and CAM-SOM using this equation are summarized in366

Table 4. However, the CCSM simulations we analyze are not in equilibrium, which may367

bias these estimates. Therefore, we also use two alternative methods to estimate radiative368

forcing, which are applicable independently of whether the simulations are in equilibrium369

or not. The Gregory method (Gregory et al. 2004; Andrews et al. 2012) regresses radiative370

flux differences (∆R’TOA) between two simulations against differences in surface temperature371

(∆Tas) to yield an adjusted radiative forcing Fa. In addition to the stratospheric temperature372

adjustment, this forcing value also includes the direct response of clouds to the change in373

carbon dioxide concentrations. A drawback of this method is that it assumes linearity374

between radiative flux and temperature changes, which does not necessarily hold for fully375

coupled GCM simulations (Andrews et al. 2012). Thus, forcing estimates show a rather376

large dependence on how many years of model simulations are included in the regression.377

Following Andrews et al. (2012) we use the first 150 years of our CCSM simulations and378

find that the adjusted forcing increases from 2.90 W m−2 for 2xCO2-1xCO2 to 4.31 W m−2379

for 8xCO2-4xCO2 (Figure 5). The regression slopes in Figure 5 do not correspond to the380

climate sensitivity values obtained using radiative kernels, since the estimates are based381

on different segments of the CCSM simulations, and the slope is not constant over the382

length of the simulation. Additionally, we compute radiative forcing by taking the difference383

between TOA fluxes obtained from offline radiative transfer calculations before and after384

CO2 concentrations are doubled. These forcing estimates are instantaneous, Fi, and do not385

take into account atmospheric adjustment (Hansen et al. 2005). Results from both methods386

15

are compared with the radiative forcing estimates from Equation (8) in Table 4. While the387

absolute forcing values are sensitive to the method used to obtain them Fa, Fi and FCCSM388

all increase with CO2 baseline amount. In CAM-SOM we first see an increase between389

the 1st and 2nd doubling and a subsequent decrease from the 2nd to the 3rd doubling.390

The prevalent positive trend of forcing is in agreement with CM09. While CM09 do not391

present the temperature change associated with each CO2 doubling, we infer from forcing392

and climate sensitivity values in their Figure 1 that surface temperature change must remain393

approximately constant, while we see an increase in surface temperature change for successive394

doublings. Model differences leading to this different temperature response may explain why395

both studies find increases in forcing, but opposite trends in sensitivity.396

6. Discussion397

We have used GCM simulations with forcings ranging from CO2 doubling to octupling398

to investigate the robustness of climate sensitivity and the contributing feedbacks in both a399

slab ocean and a fully coupled version of the NCAR climate model. We find that, in both400

model versions, climate sensitivity increases with each successive doubling in CO2 primarily401

due to an increase in positive water vapor and cloud feedbacks, while a decrease in positive402

albedo and increase in negative lapse rate feedbacks dampen this increase in sensitivity. We403

have decomposed the change in each feedback into contributions from radiative kernel and404

climate response changes. We find that while the climate response dominates the change405

in lapse rate and SW cloud feedbacks, radiative effects are more important for changes in406

water vapor and Planck feedbacks. Both play a role in the case of surface albedo and LW407

cloud feedbacks. Thus, climate sensitivity changes cannot be attributed mainly to one or408

the other factor, but are indeed the result of a combination of both.409

We further see differences in the absolute magnitudes of feedbacks between the fully coupled410

CCSM and CAM-SOM. In some cases, for the lapse rate and SW cloud feedbacks in par-411

16

ticular, feedbacks differ as much between the two model configurations as they do between412

successive doublings of CO2. These differences can amount to as much as 40% of feedback413

values, as is the case for the SW cloud feedback, suggesting caution in the interpretation of414

studies that rely solely on slab ocean model simulations to study climate feedbacks.415

Due to the long time scales necessary for adjustment of fully coupled simulations to large416

forcings and the associated computational expense, we have been able to use only one GCM417

in our analysis. The behavior of feedbacks may differ substantially for other models, as sug-418

gested by the differences between the results presented here and in CM09, for instance. This419

is a concern in particular in the case of feedbacks known to exhibit non-linear behavior, such420

as the surface albedo feedback. However, a very limited amount of data from fully coupled421

millennial-length GCM simulations driven by a wide range of forcings is available. Thus,422

intercomparisons among several models, although desirable, are not feasible at this time.423

Acknowledgments.424

We thank two anonymous reviewers for their constructive comments. This work was425

supported by NASA Headquarters under the NASA Earth and Space Science Fellowship426

Program - Grant “10-Earth10R-35”, by the National Science Foundation under Grant No.427

ATM-0904092 and by the Office of Science (BER), US Department of Energy, Cooperative428

Agreement No DE-FC02-97ER62402. Computing resources were provided by the National429

Center for Atmospheric Research (NCAR) Computational and Information Systems Labo-430

ratory (CISL). NCAR is sponsored by the National Science Foundation.431

17

432

REFERENCES433

Andrews, T., J. Gregory, M. Webb, and K. Taylor, 2012: Forcing, feedbacks and climate434

sensitivity in CMIP5 coupled atmosphere-ocean models. Geophys. Res. Lett., 39, L09 712.435

Boer, G., K. Hamilton, and W. Zhu, 2005: Climate sensitivity and climate change under436

strong forcing. Clim. Dyn., 24, 685–700.437

Boer, G. and B. Yu, 2003: Climate sensitivity and response. Clim. Dyn., 20, 415–429.438

Cess, R. and G. Potter, 1987: Exploratory studies of cloud radiative forcing with a general439

circulation model. Tellus, 39, 460–473.440

Chen, C. and V. Ramaswamy, 1996: Sensitivity of simulated global climate perturbations441

in low cloud microphysical properties. Part I: globally uniform perturbations. J. Climate,442

9, 1385–1402.443

Colman, R. and B. McAvaney, 2009: Climate feedbacks under a very broad range of forcing.444

Geophys. Res. Lett., 36, L01 702.445

Danabasoglu, G., 2004: A comparison of global ocean general circulation model simulations446

obtained with synchronous and accelerated integration methods. Ocean Model., 7, 323–447

341.448

Danabasoglu, G. and P. Gent, 2009: Equilibrium climate sensitivity: Is it accurate to use a449

slab ocean model? J. Climate, 22, 2494–2499.450

Forster, P., M. Blackburn, R. Glover, and K. Shine, 2000: An examination of climate sen-451

sitivity for idealised climate change experiments in an intermediate general circulation452

model. Clim. Dyn., 16, 833–849.453

18

Gregory, J., et al., 2004: A new method of diagnosing radiative forcing and climate senstivity.454

Geophys. Res. Lett., 31, L03 205.455

Hansen, J., et al., 2005: Efficacy of climate forcings. J. Geophys. Res., 110, D18 104.456

Jonko, A., K. Shell, B. Sanderson, and G. Danabasoglu, 2012: Climate feedbacks in CCSM3457

under changing CO2 forcing. Part I: Adapting the linear radiative kernel technique to458

feedback calculations for a broad range of forcings. J. Climate, in press.459

Raval, A. and V. Ramanathan, 1989: Observational determination of the greenhouse effect.460

Nature, 342, 758–761.461

Russel, G. L., J. R. Miller, and D. Rind, 1995: A coupled atmosphere-ocean model for462

transient climate change. Atmos. Ocean, 33, 683–730.463

Sanderson, B. and K. Shell, 2012: Model-specific radiative kernels for calculating cloud and464

non-cloud climate feedbacks. J. Climate, submitted.465

Shell, K., J. Kiehl, and C. Shields, 2008: Using the radiative kernel technique to calculate466

climate feedbacks in NCAR’s Community Atmospheric Model. J. Climate, 21, 2269–2282.467

Soden, B., A. Broccoli, and R. Hemler, 2004: On the use of cloud forcing to estimate cloud468

feedback. J. Climate, 17, 3661–3665.469

Soden, B., I. Held, R. Colman, K. Shell, J. Kiehl, and C. Shields, 2008: Quantifying climate470

feedbacks using radiative kernels. J. Climate, 21, 3504–3520.471

Stouffer, R., 2004: Time scales of climate response. J. Climate, 17, 2685–2688.472

von Storch, H. and F. Zwiers, 1988: Recurrence analysis of climate sensitivity experiments.473

J. Climate, 1, 157–171.474

Wetherald, R. and S. Manabe, 1988: Cloud feedback processes in a general circulation model.475

J. Atmos. Sci., 45, 1397–1416.476

19

Yeager, S., C. Shields, W. Large, and J. Hack, 2006: The low-resolution CCSM3. J. Climate,477

19, 2545–2566.478

Zelinka, M., S. Klein, and D. Hartmann, 2012: Computing and partitioning cloud feedbacks479

using cloud property histograms. Part I: Cloud radiative kernels. J. Climate, 25, 3715–480

3735.481

Zhang, M., J. Hack, J. Kiehl, and R. Cess, 1994: Diagnostic study of climate feedback482

processes in atmospheric general circulation models. J. Geophys. Res., 99, 5525–5537.483

20

List of Tables484

1 Feedbacks in units of W m−2 K−1 in (a) CCSM and (b) CAM-SOM for the485

2xCO2-1xCO2, 4xCO2-2xCO2 and 8xCO2-4xCO2 experiments computed from486

1000-year averages (years 451-1450) using 1xCO2, average and 8xCO2 kernels,487

compared to ”hybrid” feedbacks computed combining the 8xCO2 kernel with488

the 2xCO2-1xCO2 climate response and the 1xCO2 kernel with the 8xCO2-489

4xCO2 climate response. s is the climate sensitivity in units of K per W490

m−2. 22491

2 Differences between 2xCO2-1xCO2 and 8xCO2-4xCO2 feedbacks and climate492

sensitivity in (a) CCSM and (b) CAM-SOM. The total difference (between493

the first and third rows in Table 1a and b), as well as contributions to it from494

changes only in the kernel (difference between the first and forth rows in Table495

1a and b) and changes only in the climate response (difference between the496

first and fifth rows in Table 1a and b) are shown. 23497

3 Results of recurrence analysis for those feedbacks that show overlap between498

histograms. Xp is the 98th percentile of the feedback distribution with the499

smaller mean and T is the test statistic, i.e. the count of realizations from500

the sample with the larger mean that are larger than Xp. When T equals501

the sample size n = 100, the difference between feedbacks is found to be502

(98%,50%)-recurrent at significance level qn = 0.98100 = 0.13. 24503

4 Forcing values for the three CO2 doublings in CCSM and CAM-SOM. The504

adjusted forcing Fa is computed using the Gregory method (Gregory et al.505

2004). Instantaneous forcing Fi is calculated as the direct effect of CO2 using506

the offline radiative transfer model, and FCCSM and FCAM are obtained from507

F = ∆T as/s. All forcing estimates have units of W m-2. 25508

21

Table 1. Feedbacks in units of W m−2 K−1 in (a) CCSM and (b) CAM-SOM for the 2xCO2-1xCO2, 4xCO2-2xCO2 and 8xCO2-4xCO2 experiments computed from 1000-year averages(years 451-1450) using 1xCO2, average and 8xCO2 kernels, compared to ”hybrid” feedbackscomputed combining the 8xCO2 kernel with the 2xCO2-1xCO2 climate response and the1xCO2 kernel with the 8xCO2-4xCO2 climate response. s is the climate sensitivity in unitsof K per W m−2.

a) CCSM Planck ln(q) LR α SW C LW C Net C s2xCO2-1xCO2 (1xCO2 k) -3.10 1.57 -0.37 0.29 -0.37 0.43 0.06 0.654xCO2-2xCO2 (avg. k) -3.04 1.68 -0.41 0.24 -0.19 0.35 0.16 0.738xCO2-4xCO2 (8xCO2 k) -3.03 1.91 -0.53 0.16 -0.15 0.39 0.24 0.802xCO2-1xCO2 (8xCO2 k) -3.00 1.84 -0.39 0.26 -0.40 0.47 0.07 0.828xCO2-4xCO2 (1xCO2 k) -3.13 1.64 -0.49 0.25 -0.18 0.34 0.16 0.64

b) CAM-SOM Planck ln(q) LR α SW C LW C Net C s2xCO2-1xCO2 (1xCO2 k) -3.10 1.64 -0.48 0.26 -0.39 0.44 0.05 0.614xCO2-2xCO2 (avg. k) -3.06 1.80 -0.56 0.18 -0.31 0.43 0.12 0.668xCO2-4xCO2 (8xCO2 k) -3.03 2.03 -0.65 0.09 -0.19 0.49 0.30 0.792xCO2-1xCO2 (8xCO2 k) -3.00 1.94 -0.48 0.18 -0.38 0.51 0.13 0.818xCO2-4xCO2 (1xCO2 k) -3.13 1.74 -0.60 0.15 -0.20 0.45 0.25 0.63

22

Table 2. Differences between 2xCO2-1xCO2 and 8xCO2-4xCO2 feedbacks and climatesensitivity in (a) CCSM and (b) CAM-SOM. The total difference (between the first andthird rows in Table 1a and b), as well as contributions to it from changes only in the kernel(difference between the first and forth rows in Table 1a and b) and changes only in theclimate response (difference between the first and fifth rows in Table 1a and b) are shown.

a) CCSM Planck ln(q) LR α SW C LW C Net C stotal difference 0.07 0.34 -0.16 -0.13 0.22 -0.04 0.18 0.15due to kernel 0.10 0.27 -0.02 -0.03 -0.03 0.04 0.01 0.17due to climate response -0.03 0.07 -0.12 -0.04 0.19 -0.09 0.10 -0.01

b) CAM-SOM Planck ln(q) LR α SW C LW C Net C stotal difference 0.07 0.39 -0.17 -0.17 0.20 0.05 0.25 0.18due to kernel 0.10 0.30 0.00 -0.08 0.01 0.07 0.08 0.20due to climate response -0.03 0.10 -0.12 -0.11 0.19 0.01 0.20 0.02

23

Table 3. Results of recurrence analysis for those feedbacks that show overlap betweenhistograms. Xp is the 98th percentile of the feedback distribution with the smaller mean andT is the test statistic, i.e. the count of realizations from the sample with the larger meanthat are larger than Xp. When T equals the sample size n = 100, the difference betweenfeedbacks is found to be (98%,50%)-recurrent at significance level qn = 0.98100 = 0.13.

Feedback pair Xp TPlanck feedback (2nd to 3rd doubling) -3.027 45Lapse rate feedback (2nd to 1st doubling) -0.349 28Lapse rate feedback (3rd to 1st doubling) -0.477 100Lapse rate feedback (3rd to 2nd doubling) -0.477 100SW Cloud feedback (2nd to 3rd doubling) -0.139 42LW Cloud feedback (2nd to 1st doubling) 0.394 94LW Cloud feedback (3rd to 1st doubling) 0.416 67LW Cloud feedback (2nd to 3rd doubling) 0.394 29Net Cloud feedback (1st to 2nd doubling) 0.107 100Net Cloud feedback (2nd to 3rd doubling) 0.200 100

24

Table 4. Forcing values for the three CO2 doublings in CCSM and CAM-SOM. The adjustedforcing Fa is computed using the Gregory method (Gregory et al. 2004). Instantaneousforcing Fi is calculated as the direct effect of CO2 using the offline radiative transfer model,and FCCSM and FCAM are obtained from F = ∆T as/s. All forcing estimates have units of Wm-2.

Fa Fi FCCSM FCAM

2xCO2-1xCO2 2.90 2.54 3.38 3.614xCO2-2xCO2 3.49 3.00 3.53 3.918xCO2-4xCO2 4.31 3.59 3.72 3.77

25

List of Figures509

1 (a), (b): Global, annual average difference in TOA net radiative flux (ab-510

sorbed shortwave radiation minus outgoing longwave radiation) between each511

perturbed simulation and the unforced control run in units of W m−2, rep-512

resenting the flux imbalance at the top of the atmosphere in the perturbed513

simulations, for CCSM (a) and CAM-SOM (b). (c), (d): Global, annual av-514

erage change in surface air temperature for each CO2 doubling in units of K515

in CCSM (c) and CAM-SOM (d). 28516

2 Normalized histograms of feedbacks and climate sensitivity - binned using an517

interval of 0.01 - for the three CO2 doublings for 30-year running averages,518

separated by ten years, for model years 431-1450. Solid lines: 2xCO2-1xCO2,519

long dashed lines: 4xCO2-2xCO2, short dashed lines: 8xCO2-4xCO2. Boxes520

above the histograms represent sample means, and error bars to either side of521

boxes are standard deviations. 29522

3 Zonal distributions of 1000-year average feedbacks. Solid blue lines: full523

2xCO2-1xCO2 feedbacks, dashed red lines: full 8xCO2-4xCO2 feedbacks, dashed524

blue lines: hybrid feedbacks with 2xCO2-1xCO2 climate response and 8xCO2525

kernel, solid red lines: hybrid feedbacks 8xCO2-4xCO2 climate response and526

1xCO2 kernel. Feedbacks computed using the same kernel are represented527

by lines of the same type, while feedbacks computed using the same climate528

response are represented by lines of the same color. 30529

4 (a),(b): 500 year average albedo change in % between the 8xCO2 and 4xCO2530

simulations in CCSM and CAM-SOM and (c),(d) corresponding albedo feed-531

back in W m−2 K−1. 31532

26

5 Regression of global and annual average TOA radiative flux change ∆R′

TOA533

against surface air temperature change ∆T as for the first 150 years of CCSM534

simulations after an instantaneous doubling of CO2 from baseline concentra-535

tions of 355 ppmv (blue), 710 ppmv (green) and 1420 ppmv (orange). The536

y-intercept at ∆T as = 0 gives the adjusted radiative forcing, Fa. Forcing537

values are summarized in Table 4. 32538

27

-1

0

1

2

3

4

5

6

10 20 30 40 50 60

ΔR

TO

A [W

m-2

]

Years

0

1

2

3

4

10 20 30 40 50 60

ΔT

as [K

]

Years

-1

0

1

2

3

4

5

6

0 250 500 750 1000 1250

ΔR

TO

A [W

m-2

]

Years

2xCO2-1xCO24xCO2-1xCO28xCO2-1xCO2

0

1

2

3

4

0 250 500 750 1000 1250

ΔT

as [K

]

Years

2xCO2-1xCO24xCO2-2xCO28xCO2-4xCO2

(c) ΔTs per CO

2 doubling (CCSM) (d) ΔT

s per CO

2 doubling (CAM-SOM)

(b) RTOA

change from CNTL (CAM-SOM) (a) RTOA

change from CNTL (CCSM)

Fig. 1. (a), (b): Global, annual average difference in TOA net radiative flux (absorbedshortwave radiation minus outgoing longwave radiation) between each perturbed simulationand the unforced control run in units of W m−2, representing the flux imbalance at the topof the atmosphere in the perturbed simulations, for CCSM (a) and CAM-SOM (b). (c), (d):Global, annual average change in surface air temperature for each CO2 doubling in units ofK in CCSM (c) and CAM-SOM (d).

28

(a) (b) (c)

(d) (e) (f)

(g) (h)

Net

Fig. 2. Normalized histograms of feedbacks and climate sensitivity - binned using an intervalof 0.01 - for the three CO2 doublings for 30-year running averages, separated by ten years, formodel years 431-1450. Solid lines: 2xCO2-1xCO2, long dashed lines: 4xCO2-2xCO2, shortdashed lines: 8xCO2-4xCO2. Boxes above the histograms represent sample means, and errorbars to either side of boxes are standard deviations.

29

(a) Planck Feedback (b) Water Vapor Feedback

(c) Lapse Rate Feedback (d) Albedo Feedback

(e) LW Cloud Feedback (f) SW Cloud Feedback

(e) Net Cloud Feedback

Fig. 3. Zonal distributions of 1000-year average feedbacks. Solid blue lines: full 2xCO2-1xCO2 feedbacks, dashed red lines: full 8xCO2-4xCO2 feedbacks, dashed blue lines: hybridfeedbacks with 2xCO2-1xCO2 climate response and 8xCO2 kernel, solid red lines: hybridfeedbacks 8xCO2-4xCO2 climate response and 1xCO2 kernel. Feedbacks computed using thesame kernel are represented by lines of the same type, while feedbacks computed using thesame climate response are represented by lines of the same color.

30

(a) Albedo change in CCSM (years 951-1450)

(b) Albedo change in CAM-SOM (years 31-60)

(c) Albedo feedback in CCSM (years 951-1450)

(d) Albedo feedback in CAM-SOM (years 31-60)

-3 -2 -1 0 1 2 3 [Wm-2K-1] -17.5 -10 -5 0 5 10 17.5 [%]

Fig. 4. (a),(b): 500 year average albedo change in % between the 8xCO2 and 4xCO2

simulations in CCSM and CAM-SOM and (c),(d) corresponding albedo feedback in W m−2

K−1.

31

0

1

2

3

4

0 1 2 3 4

ΔR

’ TO

A [W

/m2 ]

ΔTas [K]

2xCO2 - 1xCO24xCO2 - 2xCO28xCO2 - 4xCO2

Fig. 5. Regression of global and annual average TOA radiative flux change ∆R′

TOA againstsurface air temperature change ∆T as for the first 150 years of CCSM simulations after aninstantaneous doubling of CO2 from baseline concentrations of 355 ppmv (blue), 710 ppmv(green) and 1420 ppmv (orange). The y-intercept at ∆T as = 0 gives the adjusted radiativeforcing, Fa. Forcing values are summarized in Table 4.

32